Duality approach to one-dimensional degenerate electronic systems

Abstract

We investigate the possible classification of zero-temperature spin-gapped phases of multicomponent electronic systems in one spatial dimension. At the heart of our analysis is the existence of non-perturbative duality symmetries which emerge within a low-energy description. These dualities fall into a finite number of classes that can be listed and depend only on the algebraic properties of the symmetries of the system: its physical symmetry group and the maximal continuous symmetry group of the interaction. We further characterize possible competing orders associated to the dualities and discuss the nature of the quantum phase transitions between them. Finally, as an illustration, the duality approach is applied to the description of the phases of two-leg electronic ladders for incommensurate filling.

53 pages, 3 figures, published version

References in corpus (14)

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• Exact duality relations in correlated electron systems
• Dynamical symmetry enlargement in metallic zigzag carbon nanotubes

Cited by in corpus (14)

• Non-perturbative methodologies for low-dimensional strongly-correlated systems: From non-abelian bosonization to truncated spectrum methods
• Phase diagrams of one-dimensional half-filled two-orbital SU(N) cold fermions systems
• Competing orders in one-dimensional half-filled multicomponent fermionic cold atoms: The Haldane-charge conjecture
• From one-dimensional charge conserving superconductors to the gapless Haldane phase
• Competing orders in the generalized Hund chain model at half-filling
• Spinful fermionic ladders at incommensurate filling: Phase diagram, local perturbations, and ionic potentials
• Resurgence and renormalons in the one-dimensional Hubbard model
• Phase diagram of one-dimensional earth-alkaline cold fermionic atoms
• One-dimensional two-orbital SU(N) ultracold fermionic quantum gases at incommensurate filling: a low-energy approach
• Edge Modes in One Dimensional Topological Charge Conserving Spin-Triplet Superconductors: Exact Results from Bethe Ansatz
• Boundary-Induced Topological and Mid-Gap States in Charge Conserving One-Dimensional Superconductors
• One-dimensional physics in transition-metal nanowires: Renormalization group and bosonization analysis
• Competing superconducting instabilities in the one-dimensional p-band degenerate cold fermionic system
• Bound-States Dynamics in One-Dimensional Multi-Species Fermionic Systems